Is there a relationship between matrix rotation and the matrix form of complex numbers

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I was going through some basic work over matrices and their different uses. I came across the matrix form of complex numbers shown as such \begin{bmatrix}a&b\\-b&a\end{bmatrix}

The next thing i looked at was the matrix rotation and found this Rotation Matrix \begin{bmatrix}cos(\theta)&-sin(\theta)\\sin(\theta)&cos(\theta)\end{bmatrix}

What is the relationship(if any) between these two different Matrices.